Issue 983 half cell

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Features
 
+-   Added DFN model for a half cell ([#1121](https://github.com/pybamm-team/PyBaMM/pull/1121))
 -   Added "R-averaged particle concentration" variables` ([#1118](https://github.com/pybamm-team/PyBaMM/pull/1118))
 -   Added support for sensitivity calculations to the casadi solver ([#1109](https://github.com/pybamm-team/PyBaMM/pull/1109))
 -   Added support for index 1 semi-explicit dae equations and sensitivity calculations to JAX BDF solver ([#1107](https://github.com/pybamm-team/PyBaMM/pull/1107))

examples/scripts/DFN_half_cell.py

@@ -0,0 +1,65 @@
+#
+# Example showing how to load and solve the DFN for the half cell
+#
+
+import pybamm
+import numpy as np
+
+pybamm.set_logging_level("INFO")
+
+# load model
+options = {"working electrode": "positive"}
+model = pybamm.lithium_ion.BasicDFNHalfCell(options=options)
+
+# create geometry
+geometry = model.default_geometry
+
+# load parameter values
+chemistry = pybamm.parameter_sets.Chen2020
+param = pybamm.ParameterValues(chemistry=chemistry)
+
+# add lithium counter electrode parameter values
+param.update(
+    {
+        "Lithium counter electrode exchange-current density [A.m-2]": 12.6,
+        "Lithium counter electrode conductivity [S.m-1]": 1.0776e7,
+        "Lithium counter electrode thickness [m]": 250e-6,
+    },
+    check_already_exists=False,
+)
+
+# process model and geometry
+param.process_model(model)
+param.process_geometry(geometry)
+
+# set mesh
+var = pybamm.standard_spatial_vars
+var_pts = {var.x_n: 30, var.x_s: 30, var.x_p: 30, var.r_n: 10, var.r_p: 10}
+mesh = pybamm.Mesh(geometry, model.default_submesh_types, var_pts)
+
+# discretise model
+disc = pybamm.Discretisation(mesh, model.default_spatial_methods)
+disc.process_model(model)
+
+# solve model
+t_eval = np.linspace(0, 3800, 1000)
+solver = pybamm.CasadiSolver(mode="fast", atol=1e-6, rtol=1e-3)
+solution = solver.solve(model, t_eval)
+
+# plot
+plot = pybamm.QuickPlot(
+    solution,
+    [
+        "Negative particle surface concentration [mol.m-3]",
+        "Electrolyte concentration [mol.m-3]",
+        "Positive particle surface concentration [mol.m-3]",
+        "Current [A]",
+        "Negative electrode potential [V]",
+        "Electrolyte potential [V]",
+        "Positive electrode potential [V]",
+        "Terminal voltage [V]",
+    ],
+    time_unit="seconds",
+    spatial_unit="um",
+)
+plot.dynamic_plot()

pybamm/expression_tree/binary_operators.py

@@ -730,6 +730,21 @@ def _binary_evaluate(self, left, right):
             return left < right
 
 
+class Modulo(BinaryOperator):
+    "Calculates the remainder of an integer division"
+
+    def __init__(self, left, right):
+        super().__init__("%", left, right)
+
+    def __str__(self):
+        """ See :meth:`pybamm.Symbol.__str__()`. """
+        return "{!s} mod {!s}".format(self.left, self.right)
+
+    def _binary_evaluate(self, left, right):
+        """ See :meth:`pybamm.BinaryOperator._binary_evaluate()`. """
+        return left % right
+
+
 class Minimum(BinaryOperator):
     " Returns the smaller of two objects "
 

pybamm/expression_tree/operations/convert_to_casadi.py

@@ -76,6 +76,8 @@ def _convert(self, symbol, t, y, y_dot, inputs):
             converted_left = self.convert(left, t, y, y_dot, inputs)
             converted_right = self.convert(right, t, y, y_dot, inputs)
 
+            if isinstance(symbol, pybamm.Modulo):
+                return casadi.fmod(converted_left, converted_right)
             if isinstance(symbol, pybamm.Minimum):
                 return casadi.fmin(converted_left, converted_right)
             if isinstance(symbol, pybamm.Maximum):

pybamm/expression_tree/symbol.py

@@ -467,6 +467,12 @@ def __abs__(self):
             pybamm.AbsoluteValue(self), keep_domains=True
         )
 
+    def __mod__(self, other):
+        """return an :class:`Modulo` object"""
+        return pybamm.simplify_if_constant(
+            pybamm.Modulo(self, other), keep_domains=True
+        )
+
     def diff(self, variable):
         """
         Differentiate a symbol with respect to a variable. For any symbol that can be

pybamm/models/full_battery_models/base_battery_model.py

@@ -189,6 +189,7 @@ def options(self, extra_options):
             "external submodels": [],
             "sei": None,
             "sei porosity change": False,
+            "working electrode": "negative"
         }
         # Change the default for cell geometry based on which thermal option is provided
         extra_options = extra_options or {}

pybamm/models/full_battery_models/lithium_ion/__init__.py

@@ -7,3 +7,4 @@
 from .dfn import DFN
 from .basic_dfn import BasicDFN
 from .basic_spm import BasicSPM
+from .basic_dfn_half_cell import BasicDFNHalfCell